Space of modular forms of level 820, weight 2, and Character 820.n

• Label: 820.2.n
• Level: $820$
• Weight: $2$
• Character orbit: 820.n
• Rep. character: $\chi_{820}(9,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $44$
• Newform subspaces: $1$
• Sturm bound: $252$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.n (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 205 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(252\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(820, [\chi])\).

	Total	New	Old
Modular forms	264	44	220
Cusp forms	240	44	196
Eisenstein series	24	0	24

Trace form

44 * q - 4 * q^11 - 10 * q^15 + 4 * q^19 - 12 * q^25 + 12 * q^29 + 8 * q^31 + 6 * q^35 - 28 * q^41 + 4 * q^45 + 32 * q^51 + 10 * q^55 - 32 * q^59 + 20 * q^65 + 28 * q^69 - 32 * q^71 + 28 * q^75 + 32 * q^79 - 52 * q^81 - 8 * q^85 + 16 * q^89 + 14 * q^95 - 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(820, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
820.2.n.a	$820$	$2$	820.n	205.j	$4$	$44$	$22$	$6.548$		None		✓	✓	✓	820.2.n.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(820, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(820, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(205, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(410, [\chi])\)\(^{\oplus 2}\)